Joint analysis of multi-level repeated measures data and survival: An application to the end stage renal disease (ESRD) data

Shared random effects models have been increasingly common in the joint analyses of repeated measures (e.g. CD4 counts, hemoglobin levels) and a correlated failure time such as death. In this paper we study several shared random effects models in the multi-level repeated measures data setting with dependent failure times. Distinct random effects are used to characterize heterogeneity in repeated measures at different levels. The hazard of death may be dependent on random effects from various levels. To simplify the estimation procedure, we adopt the Gaussian quadrature technique with a piecewise log-linear baseline hazard for the death process, which can be conveniently implemented in the freely available software aML. As an example, we analyze repeated measures of hematocrit level and survival for end stage renal disease patients clustered within a randomly selected 126 dialysis centers in the U.S. renal data system data set. Our model is very comprehensive yet easy to implement, making it appealing to general statistical practitioners.